Closed-form position analysis of variable geometry trusses
Journal Article (2017)
Mechanism and Machine Theory
Variable geometry trusses are composed, in general, of unit cells which can be modeled as bars connected by spherical joints. Under mild conditions, it has been shown that the only feasible cells are topologically equivalent to bipyramids. Unfortunately, using standard formulations, the closed-form position analysis of bipyramids is not a trivial task. Actually, it has only been achieved for bipyramids with up to 7 vertices, whose closure polynomial has been shown to be of order 24. In this paper, using a distance-based formulation and a kinematic inversion for fans of tetrahedra, the problem is solved for bipyramids with up to 11 vertices, whose closure polynomial is of degree 896. No other position analysis problem leading to such a high-order closure polynomial has been previously solved.
Variable Geometry Trusses, Position Analysis, Bipyramids,Fans of tetrahedra, Coordinate-free formulations, Distance-based formulations
J.M. Porta and F. Thomas. Closed-form position analysis of variable geometry trusses. Mechanism and Machine Theory, 109: 14-21, 2017.